Grades 6-8 — Problem-Solving Talks

Professional learning and Instructional Resources for Math Support and Intervention

Review essential concepts from grades 3-5

Preview foundational representations and strategies for grades 6-8

Overview of Problem-Solving Talks

Problem-Solving Talks are designed to review grades 3-5 concepts involving fractions, decimals, and computation while previewing foundational grade 6-8 representations and strategies for rational numbers, ratios, rates, and percents. These resources help teachers to connect review topics, such as locating and labeling fractions and decimals on number lines, directly to essential grade 6 strategies and concepts, such as representing negative rational numbers or equivalent fractions, decimals, and percents on a percent bar.

These resources are built around videos that structure a problem-solving talk with a class or small group of students. The video briefly reviews essential representations, strategies, and concepts. Then, the group or class of students completes a set of problem-solving challenges where they build representations and solve problems using a set of magnetic manipulatives on a whiteboard. Instructional notes for the video help teachers focus their questioning strategies and identify pause points in the video to address diagram comprehension, concept development, and vocabulary. Finally, students apply what they have learned through daily problem-solving tasks and practice pages.

Concept Progression for Problem-Solving Talks

Review grades 3-5 & Preview grades 6-8

Concept Progression for Problem-Solving Talks

Problem-Solving Talks Review Grades 3-5 strategies and concepts for representing whole numbers, fractions, and decimals on number lines.

Then, students are challenged to apply those grades 3-5 strategies to Preview Foundational Grades 6-8 representations, strategies, and concepts.

  • Strategies to represent whole numbers are applied to represent integers.

  • Strategies to represent fractions and decimals are applied to represent negative rational numbers.

  • Foundational ratio strategies are previewed and applied to generate equivalent ratios and solve problems.

  • Strategies to represent rational numbers on number lines are applied to represent rates on double number lines and percents on percent bars.

Problem-Solving Videos

Structure a Problem-Solving Talk

Sample PS Video — Measure to Plot and Label Positive and Negative Fractions

Problem-Solving Talks review essential concepts from grades 3-5 and preview representations and strategies from grades 6-8.

Problem-Solving Videos structure these talks by reviewing or introducing essential representations or strategies and challenging groups of students to build representations and solve problems.

For example, many students entering middle school have a weak understanding of how measurement is used to locate and label whole numbers, fractions, and decimals on number lines. The sequence of PPS Videos starts with a review of plotting whole numbers, fractions, and decimals on number lines. Then, students apply these strategies to locate and label negative integers, fractions, and decimals.

Resources for Problem-Solving Talks include a magnetic manipulative kit for whiteboards, instructional notes, application tasks, and practice pages.

Review and Preview essential representations, strategies, and concepts

REVIEW and PREVIEW — Positive and negative fractions on number lines represent their distance and direction from zero. 

REVIEW — The length of a unit-fraction bar is defined by the number of equal-length bars that measure a length of 1 on the number line. 

REVIEW — Represent fractions greater than 1 .

REVIEW — Two numbers that measure the same distance and direction from zero on a number line are said to be equivalent.

PREVIEW — Positive fractions can be reflected across the tick mark for zero to locate the opposite negative fraction.

Challenge a small group or class of students to build representaions and solve problems

Each Problem-Solving Video includes a series of problem-solving Challenges that are solved as a small group or class. Students use manipulatives from the Magnetic Manipulative Kit for whiteboards to apply strategies demonstrated in the video.

For this Problem-Solving Video, Measure to Plot and Label Positive and Negative Fractions, students:

  • Use magnetic number line segments to build the number line.

  • Apply measurement strategies from the video to plot and label fractions on the line.

  • Learn that measurement strategies to plot and label positive fractions to the right of zero can be applied to measure, plot, and label negative fractions to the left of zero.

CHALLENGE 6.3A.1

CHALLENGE 6.3A.2

CHALLENGE 6.3A.3

CHALLENGE 6.3A.4

Magnetic Whiteboard Manipulative Kit

Challenge students to build representations and solve problems

Magnetic Number Line Segments, Measurement Bars, and Fraction Strips

Drawn to scale on a 48 in by 36 in magnetic whiteboard.

Magnetic Grid and Chips, Double Number Lines, and Percent Bars

Drawn to scale on a 48 in by 36 in magnetic whiteboard.

The Video Overview and Instructional Notes outline the conceptual highlights of the Problem-Solving Videos and list the essential strategies and concepts that are introduced and reviewed. In addition, video pause points with instructional notes identify important representations, strategies, and concepts and offer suggestions for facilitating discussions and problem-solving with students.

The instructional notes offer questioning strategies for each Problem-Solving Challenge and identify other pause points with notes on:

  • Diagram Comprehension

  • Essential Concept Development

  • Vocabulary Discussion

  • Problem-Solving

Video Overview and Instructional Notes

Develop and refine questioning strategies

REVIEW Pause Points

The first three pages of this VOIN review the basics for measuring to locate and label fractions on number lines.

  • Identify unit fractions bars

  • Measure to fractions less than and greater than one.

  • Identify equivalent fractions and whole numbers that measure from zero to the same point on the line.

PREVIEW Pause Points

The Preview pause points on this page challenge students to apply the measurement strategies to plot and label negative fractions to the left of zero.

  • The mirror image of a positive fraction across zero is the opposite negative fraction.

  • Negative fractions measure a distance to the left of zero, where measurement bars represent distance and the arrows (or vectors) represent both distance and direction from zero.

  • Then, students are Challenged to use magnetic measurement bars and fraction strips to locate and label negative fractions on a whiteboard number line.

Problem-Solving Tasks and Practice Pages

Apply essential concepts and strategies

Daily Problem-Solving Tasks are represented on the whiteboard using the Magnetic Manipulative Kit so that students entering the classroom can review the tasks and solve the problem. Then, to start class, students can briefly share strategies to solve the problem. These short tasks allow teachers to review important strategies and concepts introduced in the Problem-Solving Video.

Daily Problem-Solving Tasks

The Practice Problem-Solving Pages challenge students to apply the concepts and strategies that were introduced in the Problem-Solving Video and reviewed in each Daily Problem-Solving Task.

On pages 1 and 2, students use the Equal-Parts Ruler (see below) to measure and plot fractions on number lines. On Pages 3 and 4, students interpret equally-spaced tick marks as marking off equal-length measurement bars to locate and label fractions. Students apply their understanding of measurement bars to interpret these equally spaced tick marks. This helps students to focus on the equal increments between the tick marks and not on counting the number of tick marks.

Practice Problem-Solving Pages

Students use measurement bar rulers to plot and label points on number lines on some Practice Problem-Solving Pages. These rulers allow students to practice measurement strategies introduced in the PPS Videos. Sets of rulers are printed from a downloaded PDF.

Measurement-Bar Rulers

Image of Short-Bar Ruler

Image of Equal-Parts Ruler